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In Economics 101, we are taught that the U.S. Federal Reserve Bank (the "Fed") conducts monetary policy through open market operations. These open market operations – the buying and selling of government securities – are how the Fed ultimately controls the federal funds interest rate. Why is this rate so important? Because it is one of the Federal Reserve's primary tools for preventing inflation from running rampant and controlling the peaks and troughs of a business cycle. With the current target rate for federal funds at 0–0.25%, the next time the Federal Open Market Committee (the FOMC, or policymaking committee of the Fed) changes its longstanding policy of low interest rates and finally decides on an increase is being highly anticipated. Through the federal funds futures contract, we can see the market's estimate of the probability of a change in the target federal funds rate.

In this TradeStation Labs Analysis Concepts paper, we will introduce a RadarScreen® indicator that plots the probability of a change in the federal funds rate by analyzing the federal funds futures contract price. Additionally, we will cover the basics of what a federal funds futures contract represents.

30-Day Federal Funds Futures Contract

The federal funds futures contract was introduced by the Chicago Board of Trade in October 1988. This product enables individuals and businesses to hedge increases and decreases in short-term interest rates. Each federal funds futures contract represents the average overnight federal funds rate for the contract month. This means that as the days in the current contract month pass, the more closely the futures price will represent the actual average federal funds rate for the month. This is because we already know the actual federal funds rate for some portion of the month that will be included in the average calculation for the final cash-settlement price.

Because the final cash-settlement price of the futures contract is based on the average actual daily federal funds overnight rates, the contract's volatility also decreases as it gets closer to expiration. The price of the federal funds futures contract is expressed as 100 minus the federal funds effective rate (FER). For example, if the current price of the April 2011 Federal Funds Futures contract were 99.875, the implied average FER for the month of April 2011 is 0.125%. In Figure 1 below is a table displaying how to calculate the implied average federal funds effective rates based on the current price of the federal funds futures contract.

Figure 1: Implied Federal Funds Effective Rate (FER)

Symbol

Description

Price

Calculation

Implied Average Effective Rate

FFJ11

30-Day Federal Funds Apr 2011

99.875

100 - 99.875

0.13%

FFK11

30-Day Federal Funds May 2011

99.865

100 - 99.865

0.14%

FFM11

30-Day Federal Funds Jun 2011

99.860

100 - 99.860

0.14%

FFN11

30-Day Federal Funds Jul 2011

99.845

100 - 99.845

0.16%

FFQ11

30-Day Federal Funds Aug 2011

99.815

100 - 99.815

0.19%

FFU11

30-Day Federal Funds Sep 2011

99.790

100 - 99.790

0.21%

Each federal funds futures contract expires on the last business day of the delivery month. Originally, there were 24 calendar months available; however, the Chicago Mercantile Exchange recently added another 12 months of contracts to make a total of 36 calendar months available for trading.

One primary use of the federal funds futures contract is as a hedging tool against an increase or decrease in short-term interest rates. Considering that the federal funds rate affects short-term money-market rates as a whole, the change in this rate is extremely important to the economy. Additionally, the direction and magnitude of the change of the federal funds rate reveal the FOMC's outlook for the economy. Since December 16, 2008, the FOMC has kept the target rate at an unusually low 0–0.25%, signifying its worries about the overall U.S. economy and the economy's ability to sustain growth in the absence of such an easy monetary policy.

Federal Funds Futures Contract Volatility

In the period preceding an actual change in the target rate by the FOMC, you can observe increased volatility in the federal funds futures contract. One thing to note is that FOMC meeting dates are public information that is available prior to the meetings themselves. The FOMC holds eight regularly scheduled meetings but may meet otherwise as needed, depending on the state of the U.S. economy. In Figure 2 below, you can see the increased volatility several weeks before the actual rate changes occurred. The October 8, 2008 rate decrease of 50 basis points (50 bps, or 0.5%) was made at an unscheduled FOMC meeting. The next rate decrease of 50 basis points occurred on October 29 during a regularly scheduled meeting. The purple vertical lines in Figure 2 below represent the dates of the rate changes. The volatility indicator represents the 30-day standard deviation of the continuous federal funds futures contract.

The "Great Recession," which, according to the National Bureau of Economic Research's business cycle dating committee, began in December 2007 and officially ended in June 2009, is a good example of when the FOMC had to take emergency measures to help the economy from experiencing worsening economic turmoil. However, the increased volatility of the federal funds futures contract also occurs during less extreme economic times, when the Fed is adjusting the target federal funds rate. This is evident in Figure 3 below.

Figure 3: Volatility of Fed Funds Futures Contract September 2005

Probability of Federal Funds Rate Change

The formula used in this indicator to determine the probability of a change in the target federal funds rate was derived from a 1997 CBOT white paper titled, "Insights Into Pricing the CBOT Fed Funds Futures Contract." The CBOT later merged with the Chicago Mercantile Exchange, so the federal funds futures contract currently resides on that exchange. Although the white paper was written many years ago, the basic formula can still be applied today to gauge the market's view of the probability of a Fed rate hike or discount at the next meeting.

Figure 4 below is an image of how the indicator appears in RadarScreen. There are five different plots in this indicator.

The first plot, "Fed Change," displays the actual probability of a change in the target federal funds rate based on the current price of the federal funds futures contract, the date of the FOMC meeting in the contract month, and the target rate you define as an input.

The second plot, "No Change," is simply 100 minus the probability of the change displayed in the first plot.

The third plot, "Target Rate," is an input of the indicator, which you define based on your expectation for the next target rate change. For example, the most likely change by the Fed when it next decides to increase the target rate may be an increase to 0.50%. In Figure 4, the target rate is identified as 0.50% and indicates that as of March 30, 2011, the date by which the Fed is most likely to increase the rate to this level is the March 2012 FOMC meeting (100% probability in the "Fed Change" column).

The fourth plot, "Current Rate," is the current target federal funds rate, which at this time is defined as 0-0.25%. The value of 0.13% is used to represent the current target federal funds rate.

The final plot shows the implied federal funds effective rate (FER) based on the current price of the futures contract.

There are several things to consider when analyzing this indicator, including that the probability may change often and dramatically depending on various factors. U.S. economic news, speeches from different Federal Reserve members, and other factors may cause the probability to change drastically from one day to another. Also, the indicator cannot be used on the federal funds continuous futures contract. However, you may use the indicator at any interval in RadarScreen.

Inputs

The names and descriptions of the inputs included in this indicator are listed below in Figure 5. The first input, "ExpectTargetRate," is the rate to which you believe the FOMC is going to raise or lower the target federal funds rate. In the current market environment, the Federal Reserve may raise the target federal funds rate to 0.50%. If inflation is much higher than expected, it may choose to increase the rate to 0.75%. If you would like to see the probability of the Fed raising the target rate to 0.75%, you would adjust the "ExpectTargetRate" input to 0.75. The second input, "CurrentRate," is used to define the current target federal funds rate. As of the writing of this paper, the current target federal funds rate is 0-0.25%. However, once monetary policy changes, you can adjust the "CurrentRate" input to represent the new target interest rate.

The last input in Figure 5 represents 16 different inputs that were created to allow you to adjust the FOMC dates as they are released. The date format is identified in the name of the input as "YYMMDD." Once the 2013 dates are released, you can adjust the first eight meeting date inputs with the 2013 dates. Notice below the default for the first meeting is "110126," which represents January 26, 2011, as that was the first FOMC meeting date in 2011.

Figure 5: Inputs

Name

Default

Description

ExpectTargetRate

1.00

The target federal funds rate you expect the Federal Reserve to choose at the next FOMC meeting.

CurrentRate

0.25

The current target federal funds rate chosen by the FOMC.

MeetingDate1_YYMMDD

110126

The FOMC meeting dates available on the Federal Reserve website.

Calculation

In order to illustrate the formula and calculation behind the probability of a change in the federal funds rate, we will concentrate on the example of the indicator in Figure 6 below. The image displays the indicator applied to the January 2012 Federal Funds Futures contract. Based on the different variables, the probability of a federal funds rate change to 0.50% from a current rate of 0.13% is 61.33%.

Figure 6: Probability of a Rate Hike to 0.50% in January 2012

Figure 7 below details the calculation of the probability of a change. The letter "a" in the formula below represents the actual probability. The equation breaks down the current implied average federal funds effective rate to determine the probability. We know the current target rate as defined by the most recent FOMC decision. The portion of the month the target rate is known is based on the day of the FOMC meeting in the contract month. In this example, the day of the FOMC meeting in January 2012 is January 25. Therefore, for most of the month we know the current target rate. The next part of the equation will use the portion of the month the target rate is unknown and multiply it by the probability of a change times the expected target rate plus the probability of no change times the current target rate.

Figure 7: Formula

If the FER is below your expected target rate, then logically the probability of a federal funds rate increase will be less than 100%. Notice in Figure 6 that the implied FER is 0.36%, but the expected target rate we chose was 0.50% and, appropriately, the probability of a Fed rate change is less than 100 at 61.33%.

An additional point of information is that FOMC meetings are not held every month. They are held eight times a year, plus any emergency meetings deemed necessary by the FOMC. That does not necessarily mean that there is a 0% chance of a change in the federal funds rate during the months when no meeting is scheduled, because there is always the possibility that an emergency meeting can be held.

A drawback to the equation's use of the actual dates of the FOMC meeting as part of its calculation is that the inputs for the meeting dates will need to be updated in the future. As of this writing, the available dates on the Federal Reserve website, http://www.federalreserve.gov/monetarypolicy/fomccalendars.htm#11655, are posted only through 2012. If any changes occur to the schedule or the 2013 meeting dates become available, the inputs will need to be updated.

Conclusion

Although the FOMC has taken abnormal measures in keeping the target federal funds rate at 0-0.25% for more than two years running, there is no doubt that it will have to reverse course and start to increase rates eventually. If the U.S. economy continues to create jobs and economic growth returns to normal, the Fed will have no choice but to start increasing rates. With the use of the federal funds futures contract, we can be better informed and hopefully anticipate this rise. Understanding and anticipating the Federal Reserve's moves may help you determine the direction of short-term interest rates.

With the Probability of a Fed Change indicator, you can now use the price of a federal funds futures contract to calculate the chances of a change occurring. The inputs "ExpectTargetRate" and "CurrentRate" allow you to identify what you expect the new rate to be, as well as the current target federal funds rate. Remember that you cannot use the federal funds continuous futures contract when placing this indicator in RadarScreen, and the interval chosen does not affect the indicator's result. There are many different financial websites (including CME, CNBC, and Bloomberg) that publish the probability of a change in the federal funds rate. However, this indicator allows you to monitor this important value directly in TradeStation.

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